Question

Velocity vs displacement graph for a body is shown in the figure.

Find the acceleration of body when it's displacement is $10\text{m}$, considering $1\text{D}$ motion along a straight line.

• A. $10{\text{m/s}}^2$
• B. $-10{\text{m/s}}^2$
• C. $5{\text{m/s}}^2$
• D. $-5{\text{m/s}}^2$

Answer 1

The correct option is D $-5{\text{m/s}}^2$

The relation between acceleration $\left(a\right)$ and displacement($s$) is expressed as:
$a=v\frac{dv}{ds}.............\left(i\right)$
Hence, at any value of $s$ the, acceleration is given by:
$a=v\times$ (slope of ($v-s$) graph)
where, $v=$ velocity at that position.
$\Rightarrow {\text{(Slope of graph)}}_{s=10\text{m}}=\frac{10-0}{5-15}=-1$ $\because$ slope of graph is -ve and constant for $s=5\text{m}$ to $s=15\text{m}$
From graph
$v_{s=10\text{m}}=5\text{m/s}$
$\therefore a=\left(v_{s=10\text{m}}\right)\times {\text{(Slope of graph)}}_{s=10\text{m}}$
$\Rightarrow a=5\times -1=-5{\text{m/s}}^2$